Regarding averaging down, or doubling up on a trading position, there is no problem with doing that, so long as you plan your trades and trading size accordingly, and that is your plan in advance. Thus, if you are willing to commit $50,000 to a position, and you want to leave open the fleixibility of averaging down, then your initial purchase should be for no more than $25,000. If you want to leave open the flexibility of taking up to four positions, then each should be no more than $12,500. If you note, Zeev trades about 2000 stocks at once - LOL, actually probably 12-20. He also averages perhaps 50% cash. Thus, I expect that each trade is in the range of 1-2% of his equity. Thus, even if he takes four helpings of a stock, the position will only account for about 4-8% of his equity, which is not enough to paint himself into a corner.
If the initial position is more than 5-10% of your equity, I would definitely not double up.
Carl